Expand 10w(5w – 3)

**solution**
= 10w(5w – 3)

= (10w x 5w) – (10w x 3)

= 50w

^{2}– 30w*answer*

**TRY THIS………..**
Expand 4y(9y+ 10)

Expand 10w(5w – 3)

= 10w(5w – 3)

= (10w x 5w) – (10w x 3)

= 50w^{2} – 30w *answer*

Expand 4y(9y+ 10)

If
u = 20i + 2j and v = 3i + 10j find 5u + 3v

=
5u + 3v

=
5(20**i **+ 2**j**) + 3(3**i** + 10**j**)

= 100**i**
+ 10**j** + 9**i** + 30**j**

= (100**i**
+ 9**i**) + (10**j** + 30**j**)

= 109**i**
+ 40**j**

If
u = 4**i** + 3**j** and v = 2**i** + 4**j**; find 2**u** +
3**v**.

If F(x) = log_{2}x,
Find F(^{1}/ _{8192})

F(x) = log_{2}x

F(^{1}/8192) = log_{2}(^{1}/ _{8192})

F(^{1}/8192) = log_{2} 8192^{-1}

F(^{1}/8192) = log_{2}(2^{13})^{-1}

F(^{1}/8192) = log_{2}2^{(13} ^{x} ^{-1)}

F(^{1}/8192) = log_{2}2^{-13}

F(^{1}/8192) = -13log_{2}2

F(^{1}/8192) = -13 x 1

F(^{1}/8192) = -13

If F(x) = log_{5}x,
Find F(^{1}/_{3125})

A number is chosen at random
from 1 – 15 inclusive. Find the probability that it is a multiple of five or an
even number greater than 8.

Let n(S) represent sample
space

P(E) = probability of even
number greater than 8

P(M) = probability of a
multiple of 5

n(S) = {1, 2, 3, 4, 5, 6, 7,
8, 9,10, 11, 12, 13, 14, 15} = 15

n(E) = {10, 12, 14} = 3

n(M) = {5, 10, 15} = 3

But 10 appears on both
categories.

P(E) = ^{3}/15

P(M) = ^{3}/15

P(EnM) = ^{1}/15

………………………….

P(EuM) = P(E) + P(M) - P(EnM)

P(EuM) = ^{3}/15 + ^{3}/15
-^{1}/15

= ^{5}/15

= ^{1}/3 after simplification

∴ **P(EuM) = **^{1}/5

A number is chosen at random
from 17 – 30 inclusive. Find the probability that it is a multiple of 5 or an
even number.

Factorize 289x^{2 }- 169y^{2}

we use difference of two squares a^{2} – b^{2} = (a - b)(a + b)

289x^{2}- 169y^{2}
= 17^{2}x^{2}^{ }- 13^{2}y^{2}

=
(17x)^{2}^{ }- (13y)^{2}

=
(17x - 13y)( 17x + 13y)

factorize 121c^{2}- 49d^{2}

Multiply 2x - 4y by -5a

= -5a(2x - 4y)

= (-5a x 2x) - (-5a x 4y)

= (-10ax) - (-20ay) [since -5a **x** 4y = -20ay ]

= -**10ax + 20ay**

Multiply 40p - 3q by -4m

If 5^{2w}
(40^{w}) = 10^{w+40} ; Find w.

5^{2w}
(40^{w}) = 10^{w+40}

(5^{2})^{w}
(40^{w}) = 10^{w+40}

(25)^{w}
(40^{w}) = 10^{w+40}

(25 x 40)^{w}
= 10^{w+40}

(1000)^{w}
= 10^{w+40}

(10^{3})^{w}
= 10^{w+40}

3w = w+40

3w - w = 40

2w = 40

If 3^{2t}
(4^{t}) = 6^{t+10 }; Find t.

x is
directly proportional to y. x=12 while y=4. Find y when x is 69.

x ⍺ y

x = ky

12 = k x 4

4 4

k = 3

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k = 3, y= ?
x = 69.

69 = 3 x y

3 3

x is
directly proportional to y. x=20 while y=5. Find y when x is 68.

If log 2= 0.3010; find the value of log 400,000 without using
tables.

=log200,000

=log(4 x 100,000)

=log4 + log100,000

=log2^{2} + log10^{5}

=2log2 + 5log10

=2(0.3010) + (5 x 1) [since
log10=1 and Log3=0.3010]

=(0.6020) + 5

=5.6020

If log 2= 0.3010; find the value of log 4,000,000 without
using tables.

If 13w^{2}
= 325; find w

13w^{2} = 325

13 13

w^{2}
= 25

w = 5 Because the square root of 25 is 5.

If 14y^{2}
= 5600; find y.

A
regular polygon has 27 sides. Find the total interior angles of that polygon.

n
= 27

Total
angles = (n - 2)180^{0}

=
(27 – 2)180^{0}

=
25 x 180^{0}

=
4500^{0}

A
regular polygon has 38 sides. Find the total interior angles of that polygon.

If 8^{10}
= 32^{a-2}; find a

8^{10}
= 32^{a-2 }

(2^{3})^{10}
= (2^{5})^{a-2 }

2^{30}
= 2^{5(a-2) }

2^{30}
= 2^{5a-10 }

30 = 5a – 10

30 + 10 = 5a

40 = 5a

5 5

8 = a

If 5^{10}
= 625^{h-2}; find h

What must be added to x^{2 }+ 20x to make the expression a perfect
square?

a=1, b=20,c=?

b^{2} = 4ac

(20)^{2} = 4 x 1 x c

400 = 4c

4 4

100 = c

What must be added to x

Factorize
completely mc + mr - cr - c^{2}.

=
mc + mr - cr - c^{2}.

=
(mc + mr) – (cr - c^{2}). [Grouping the
factors]

=
m(c + r) - c(r + c). [after factoring
out]

Convert
53734m into km.

1km
= 1000m

? = 53734m

After
cross-multiplying;

=
__1 x 53734__

1000

=
__53734__

1000

=
53.734 km

Convert
72682m into km.

x is directly proportional
to y. x=32 while y=4. Find y when x is 736.

x ⍺ y

x = ky

32 = k x 4

4 4

k = 8

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k = 8, y= ? x = 736.

x = ky

736 = 8 x y

8 8

x is directly proportional
to y. x=40 while y=4. Find y when x is 380.

Estimate
the value of 2.1 x 0.034

=
2.1 x 0.034

=
2.0 x 0.03 [
2.1 ≈ 2.0 to ones and 0.034 ≈ 0.03 to hundredths]

=
0.06

Estimate
the value of 5.4 x 0.073

If
log_{3}(10x - 23)=3; find x.

log_{3}(10x
- 23)=3

(10x - 23)=3^{3 }

10x - 23=27

10x
= 27 + 23

10x
= 50

x = 5

Find a linear function f(x) with
gradient -6 which is such that f(5)=14.

m=-6, points = [5,14] and [x, f(x)]

m = y_{2}-y_{1}/x_{2}-x_{1}

-6 = [f(x) – 14]/x-5

f(x)-14=-6(x-5) [after cross multiplying]

f(x)-14=-6x+30

f(x)=-6x+30+14

f(x)=-6x+44

Give out a linear function f(x) with
gradient -4 and f(5)=11.

Simplify Log_{2}256 - Log_{3}243

= Log_{2}256 - Log_{3}243

= Log_{2}2^{8} - Log_{3}3^{5 } [Since 256=2^{8} and 243=3^{5}].

= 8Log_{2}2 - 5Log_{3}3 [since Log_{a}a = 1]

= (8 x 1) - (5 x 1)

= 8 - 5

= 3

Hence Log_{2}256 - Log_{3}243 =
3

Simplify Log_{2}1024 – Log_{5}625

If 4x + 5y -9 = 0; find
x-intercept.

x-intercept is when y=0.

4x + 5y -9 = 0

4x + 5(0) - 9 = 0

4x - 9 = 0

4x = 0+ 9

4 4

x= ^{9}/4

If 11x - 5y - 19 = 0; find
x-intercept.

An
interior angle of a regular polygon is 78^{0} greater than an exterior
angle. Find the interior angle.

Let
i = interior angle, e = exterior angle.

Now
i + e=180^{0}…………………(1)

But
i = e+78^{0 }…………………(2)

Substitute
(2) in (1) above.

e+78^{0
} + e=180^{0}

e+
e+78^{0 } =180^{0 }

2e+
78^{0 } =180^{0 }

2e=180^{0
}- 78^{0 }

2e=102^{0
}

2 2

e
= 51^{0}

From
(1),

i + e=180^{0}

i + 51=180^{0}

i =180^{0} - 51^{0 }

An
interior angle of a regular polygon is 86^{0} greater than an exterior
angle. Find the interior angle.

If n(A)= 78 , n(B)= 90 and n(AuB)= 130,
find n(AnB).

n(AuB) = n(A) + n(B) - n(AnB)

130 = 78 + 90 - n(AnB)

130 = 168 - n(AnB)

130 - 168 = - n(AnB)

-38 = -n(AnB)

n(AnB) = 38 [after dividing by -1 both
sides]

If n(A)= 71 , n(B)= 88 and n(AuB)= 130,
find n(AnB).

Simplify __60__

125^{-2/3}

= __60__

125^{-2/3}

= 60
x __1__

125^{-2/3}

=
60 x 125^{2/3 } [Since 1/a^{-n}
= a^{n}]

=
60 x (125^{1/3})^{2} ^{ } [Since
125^{1/3} = cube root of 125 = 5]

=
60 x (5)^{2} ^{ }

=
60 x 25 since (5)^{2} = 25

Simplify __20__

216^{-2/3}

Rayan deposited the amount of 30,000/=
in a bank for 4 years and got a profit of 8400/=. Find the interest rate.

I = 8400/=, P = 30,000/=, T = 4 years,
R = ?

I =__ PRT__

100

8400 = __30,000 x R x 4__

100

8400 = __30,0__~~00~~ x R x 4

1~~00~~

8400 = 300 x R x 4

8400 = 1200R

Rayan deposited the amount of 7,000/=
in a bank for 3years and got a profit of 1260/=. Find the interest rate?

Evaluate 1882^{2} – 1118^{2}

We apply difference of two squares: a^{2}
- b^{2} = (a-b)(a+b).

1882^{2} – 1118^{2}= (1882 + 1118)(
1882 - 1118)

=
(3000)( 628)

= 1884000

Evaluate 1544^{2} – 1456^{2}

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